## Financial Time Series Analysis giberrish-Tasy

### February 23, 2010

I just finished re-reading Tasy’s Finanical Time series analysis, here is a list of points worth taking notes of:

- What time series analysis is trying to model here is f(x_t|F_t-1), so what we are trying to understand here is how mean and variance related to the past, through ACF.
- portmanteau Test Q(m) (Ljung-Box stats for testing sufficiency of model) i.e. residue of dynamics, i.e. no series correlation no conditional heteroscedasticity). Q(m) ~ X^2(m) link to p stats to reject null hypothesis( no series corr in residue, no CH in residue square etc.)
- model identification( PACF or Akaike Information Criteria) -> parameter estimation (OLS with significant level of parameter estimated)-> model checking ( check if residue series is close to white noise, using Ljung-box Q(m) ~X^2(m-order(AR model used))->conditional forcast with model(i.e. error in model is not taken into account).
- unit-root nonstationary, long memory, ARIFIMA(d), ARIMA(1), dicky fuller test for unit root. Ljung-box test, look at ACF, same effect.
- seasonality model, ACF contains information for AR and seasonality. (i.e. a tool to detect seasonality & predict shape of futures curve).
- nonlinearity test( Q, BDS, F, Threshold Test), parametric( TAR, Markov switch model), nonparametric( NN, kernel, MCMC etc.
- nonsynchronize trading, var(r_o) v.s. var(r). bid ask bounce, and high frequency dynamics(negative lag-1 AR)
- order prohibit model(lo et. al.),A Decomposition Model(ADS)* ( using partition I(i) indicative function and MLE to estimate parameters) ; duration model( using combination of quadratic function to remove duriual effect), using ACR model with exponential or generalized gamma innovation; non-linear duration model with two regime. bivariate model for both price change and duration( with method similar to ADS, this is close to what altreva is doing, i.e. simulate the market)
- cross-correlation matrix contains linear dependency information( couple, direct, independent) .
- VAR model able to absorb all dynamic dependency and concurrent dependency information into transition matrix, with cholesky decomposition. stationary condition, how to test for cointegration in real applicaton, Tasy mentioned about difficulty. And erro correction form( still fuzzy about this concept).
- PCA, FA, MCMC

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